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Arthur T Knackerbracket has found the following story:
Professor Peter Coveney, Director of the UCL Centre[*] for Computational Science and study co-author, said: "Our work shows that the behaviour of the chaotic dynamical systems is richer than any digital computer can capture. Chaos is more commonplace than many people may realise and even for very simple chaotic systems, numbers used by digital computers can lead to errors that are not obvious but can have a big impact. Ultimately, computers can't simulate everything."
The team investigated the impact of using floating-point arithmetic -- a method standardised by the IEEE and used since the 1950s to approximate real numbers on digital computers.
Digital computers use only rational numbers, ones that can be expressed as fractions. Moreover the denominator of these fractions must be a power of two, such as 2, 4, 8, 16, etc. There are infinitely more real numbers that cannot be expressed this way.
In the present work, the scientists used all four billion of these single-precision floating-point numbers that range from plus to minus infinity. The fact that the numbers are not distributed uniformly may also contribute to some of the inaccuracies.
First author, Professor Bruce Boghosian (Tufts University), said: "The four billion single-precision floating-point numbers that digital computers use are spread unevenly, so there are as many such numbers between 0.125 and 0.25, as there are between 0.25 and 0.5, as there are between 0.5 and 1.0. It is amazing that they are able to simulate real-world chaotic events as well as they do. But even so, we are now aware that this simplification does not accurately represent the complexity of chaotic dynamical systems, and this is a problem for such simulations on all current and future digital computers."
The study builds on the work of Edward Lorenz of MIT whose weather simulations using a simple computer model in the 1960s showed that tiny rounding errors in the numbers fed into his computer led to quite different forecasts, which is now known as the 'butterfly effect'.
[*] UCL: University College London
Journal Reference:
Bruce M. Boghosian, Peter V. Coveney, Hongyan Wang. A New Pathology in the Simulation of Chaotic Dynamical Systems on Digital Computers. Advanced Theory and Simulations, 2019; 1900125 DOI: 10.1002/adts.201900125
(Score: 0) by Anonymous Coward on Thursday September 26 2019, @01:06AM (6 children)
Your ideas are intriguing and I'd like to subscribe to your newsletter...
Actually, I'm being semi-serious here. Why is this axiomatic? I can imagine some simple state (say a box with 2 atoms in space), and then having a giant supercomputer with numerous optimizations running some simulation on it. Why can't it go faster-than-real-time (not unlike fast-forwarding a video)?
I agree that for any practical situation with our current knowledge of physics and technology that it's not feasible. But theoretically... why is this so axiomatic as to be considered "rule zero?"
(Score: 3, Interesting) by c0lo on Thursday September 26 2019, @01:33AM (5 children)
Because the speed of light being the absolute limit of interaction speed is axiomatic.
You will make implicit assumption on the enclosure (thing like: perfect smoothness, homogenous and always the same properties affecting collisions, etc).
The reality: your box is made of atoms vibrating in a way you don't perfectly know, so you can't model them. And your box is far from isolated from the environment and will let pass or may react in ways that can perturb your experiment whenever a high-energy cosmic ray strikes it, or when quantum fluctuations of the void happens.
Your "simple state" is already a model which have predictive power on average space or time spans. It will inevitable start to diverge when you are past the limits your assumptions are valid (e.g. in 10^6 years, your box may be just dust).
https://www.youtube.com/watch?v=aoFiw2jMy-0 https://soylentnews.org/~MichaelDavidCrawford
(Score: 0) by Anonymous Coward on Thursday September 26 2019, @02:59AM (3 children)
Or consider a box with no particles in it. Boom! The universe suddenly appears. Shit happens that isn't in your model.
(Score: 2) by c0lo on Thursday September 26 2019, @03:44AM (2 children)
FTFY.
Very likely the Big Bang didn't even need a box.
https://www.youtube.com/watch?v=aoFiw2jMy-0 https://soylentnews.org/~MichaelDavidCrawford
(Score: 2) by JoeMerchant on Thursday September 26 2019, @03:02PM (1 child)
Hard to know from inside this particular box/no box universe.
🌻🌻 [google.com]
(Score: 2) by c0lo on Thursday September 26 2019, @10:05PM
Yeah, we might be dead or alive, until someone look at us.
https://www.youtube.com/watch?v=aoFiw2jMy-0 https://soylentnews.org/~MichaelDavidCrawford
(Score: 3, Informative) by JoeMerchant on Thursday September 26 2019, @02:58PM
Applicable: https://dilbert.com/strip/2019-03-03 [dilbert.com]
🌻🌻 [google.com]